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Re: tortoise algorithms



At 12:40 PM -0400 8/30/03, John S. Denker wrote:

On 08/30/2003 11:26 AM, Michael Edmiston criticized
Zeno's "paradox", saying:
> I have periodically argued with local math professors that we do not
> need an infinite series to "solve the puzzle" because there isn't any
> puzzle in the first place.

Indeed. It is disappointing that the topic could even come up.

> Therefore it amazes me there are many web sites that claim the
> Achilles/Tortoise puzzle continues to baffle scientists and
> mathematicians.

Mathematicians feel the need to cover infinite series arguments in great detail in order to justify the calculus that physics respects so much.

Zeno used the 'dumb jock' Achilles as the butt of his joke - this also appeals to many math professors. Convincing the general populace (and perhaps a few dumb jocks) that the infinite and the infinitesimal are important elements of the 'real world' is not an easy task. In point of fact - many top echelon mathematicians DON'T accept the concept of the infinite and the infinitesimal.
Accepting these ideas leads to the irrefutable Banach-Tarshi paradox.

Banach, S. and Tarski, A. "Sur la décomposition des ensembles de points en parties respectivement congruentes." Fund. Math. 6, 244-277, 1924.

If any of YOU do accept the infinitesimal mathematics - then you should be ready to 'cut' a cue ball into six well defined pieces (sets) and then reassemble them to produce two balls, identical to the first with no points left out etc.

Let's not criticize Zeno and the current batch of math professors if _*WE*_ are not willing to examine the 'correctness' of the infinitesimals.

Lot's of Google hits from .edu sites on Banach-Tarski and such.

If you EVER take advantage of an infinite series - then you too should be sharing Achilles befuddlement, presented so clearly by Zeno.


Nomex suit is zipped tight ;-)
--
I never teach my pupils; I only attempt to provide the conditions in which they can learn.
- Albert Einstein